"A woman who expends her energy exercising the brain," proclaims the psychiatrist Dr Henry Maudsley in the opening scene of this new play by Jessica Swale, "does so at the expense of her vital organs." It is a key taster of the level of opposition faced by the first generation of female students at Cambridge University, whose fight to win the right to graduate is fascinatingly depicted here through the experiences of a group of students at Girton College in 1896.

Swale is an accomplished director, especially of 18th-century comedy, and her experience shows: this is an assured Globe debut, neatly directed by John Dove, with many fine performances (as Maudsley, Edward Peel exudes all the boo-hiss nastiness of a pantomime villain). Swale's exposition feels a little clumsy at times, and the action occasionally veers close to soap opera, but she deserves credit for tackling this vital period of British educational history.

As a direct beneficiary of these pioneering women's struggles – I graduated from Clare College in 2004, when several of the elderly fellows were still rumoured to wear black armbands to mark their displeasure at the college's admittance of women – I couldn't fail to be moved. But you certainly don't need to have been to Cambridge, or indeed any university, to engage with the theme of education as a cornerstone of freedom. "The only thing a woman can own," says Girton principal Elizabeth Welsh (Gabrielle Lloyd), "is knowledge." In a world where many women are still denied the basic right to an education, her words carry a heavy weight.